What about a Royal Caribbean or Norwegian cruise out of Galveston? I know its not Disney, but they still have stuff to do for 3 year olds.
Beach wise locally I like South Padre. I like staying at the Courtyard as if you get one step up from the entry level room, the rooms are huge. Nice resort style pool, and then directly on the beach. It's also next to the pier so you can get out of the sun without having to rent an umbrella.
With that age, I probably wouldn't fly but rather due something within driving distance. I also love the JW Marriott in San Antonio Hill Country. Great pools and they have daily activities for kids.